Details

sample29.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 2.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

2.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

19.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

39.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

14.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series55.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

23.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

12.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify142.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1439	12925
1	5002	12452

prune1.3s

Filtered

269 candidates to 459 candidates (-70.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	451	8	459
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	452	8	460

Merged error: 1.0b

Counts

460 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (+ alpha beta))
0.0b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.6b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
217×	`*-un-lft-identity`
158×	`add-sqr-sqrt`
135×	`add-cube-cbrt`
82×	`associate-l`
40×	`distribute-lft-out`
37×	`difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
26×	`associate-/r/`
22×	`associate-r` `associate-/l*`
18×	`flip3-+` `flip-+`
13×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
7×	`prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
6×	`swap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/` `associate-/l/`
2×	`flip3--` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 312

Calls

4 calls:

8.0ms	(* (+ alpha beta) (+ alpha beta))
62.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
26.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ alpha beta) (+ alpha beta))
40.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
24.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify100.0ms

Algorithm

egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1491	7486
1	5001	7062

prune1.1s

Filtered

231 candidates to 324 candidates (-40.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	324	8	332

Merged error: 1.0b

Counts

332 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/l/`
7×	`times-frac` `associate-/r*`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

25.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series80.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	413	1532
1	1296	1439
2	5001	1406

prune443.0ms

Filtered

81 candidates to 93 candidates (-14.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 1.0b

Counts

101 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.6b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1185×	`times-frac`
812×	`*-un-lft-identity`
518×	`add-sqr-sqrt`
510×	`add-cube-cbrt`
480×	`sqrt-prod`
280×	`cbrt-prod`
150×	`distribute-lft-out`
71×	`associate-/l*`
70×	`associate-/r/`
43×	`flip3-+` `flip-+`
35×	`div-inv`
14×	`cbrt-div`
13×	`associate-/r*`
12×	`add-exp-log`
11×	`pow1`
9×	`swap-sqr` `add-cbrt-cube`
7×	`associate-r` `associate-l`
6×	`pow1/3`
5×	`associate-/l/`
4×	`frac-times` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `sqrt-div` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 649

Calls

4 calls:

17.0ms	(* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
43.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
332.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify219.0ms

Algorithm

egg-herbie

Counts

661 → 661

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1667	22175
1	5001	21631

prune5.7s

Filtered

397 candidates to 661 candidates (-66.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	661	0	661
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	661	8	669

Merged error: 1.0b

Counts

669 → 8

regimes131.0ms

Accuracy

51.2% (1.7b remaining)

Error of 2.9b against oracle of 1.2b and baseline of 4.7b

bsearch21.0ms

Steps

Iters	Range		Point
8	7.484628461453434e+157	1.6325587929699147e+162	7.639639112690997e+157

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	25
1	31	25

end0.0ms

sample814.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 100%

Results

479.0ms	8000×	body	80	valid
133.0ms	8000×	pre	80	true

Details

sample29.0ms

simplify82.0ms

prune3.0ms

localize12.0ms

rewrite106.0ms

series55.0ms

simplify142.0ms

prune1.3s

localize17.0ms

rewrite127.0ms

series79.0ms

simplify100.0ms

prune1.1s

localize19.0ms

rewrite49.0ms

series80.0ms

simplify44.0ms

prune443.0ms

localize19.0ms

rewrite145.0ms

series377.0ms

simplify219.0ms

prune5.7s

regimes131.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample814.0ms

Profiling